I've seen the phrase "en effet" beginning a French sentence on occasion, and I was wondering whether it was closer to the meaning of the English word "indeed" or the phrase "in effect" - or perhaps it can it have both senses? In English the two have a somewhat different meaning. "Indeed" emphasizes something previously mentioned:

I like watching tennis. Indeed, I went to Wimbledon last year.

Whereas "in effect" means that something has a particular outcome which may not be obvious, or stated explicitly previously:

Smoking is unhealthy in all sorts of ways. In effect, it's a slow means of suicide.

Indeed can also indicate confirmation or agreement. En effet and (more commonly, I think) effectivement can be used for that as well.

Was it you I saw in London yesterday? — Indeed I was in London yesterday, so that could have been me.Est-ce toi que j'ai vu à Londres hier ? — Effectivement, j'étais à Londres hier, donc il se peut que ce fût moi.

In fact can introduce a clarification (overlapping with *indeed), but most often the clause that contains in fact extends the clause it illustrates in some manner. Then en effet cannot be used; en fait or de fait* are possibilities (par le fait and dans le fait are others, but they are rare and dated). There is a nuance between en fait and de fait: en fait can convey opposition (there may be a difference between theory and practice), whereas de fait does not (practice confirms theory). Also, en fait insists on the passive aspect of fact (something is true), whereas de fait insists on the active aspect of fact (something happens).

Gravity tells us that objects fall, and in fact if you drop a stone, it falls.La pesanteur nous dit que les objets tombent, et de fait, si on lâche une pierre, elle tombe.